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What Division Means · Set 2 · Grade 3
Arrays: Division You Can See
An array is anything lined up in rows and columns.
One array answers three questions at once.
One array answers three questions at once.
5 in each row
3 rows
15 in all
3 × 5 = 15
How many in all?
15 ÷ 3 = 5
3 rows. How many in each row?
15 ÷ 5 = 3
5 in each row. How many rows?
Egg cartons, muffin tins, window panes, keyboard keys: the world is full of arrays. This set teaches you to read them.
Roots of Reason
Arrays · Set 2
Name
Date
From a Pile to an Array
A pile hides its number. An array shows it.
1.Here is a messy pile of 15 buttons. Draw them again in the box as 3 equal rows. Cross off each button as you use it.
the pile
→
your 3 rows
Each row has buttons. 15 ÷ 3 =
2.Now the other direction: take 12 buttons and make rows of 4. Draw the array. How many rows did you need?
12 ÷ 4 = rows
Roots of Reason
Arrays · Set 2
Name
Date
Turn It Sideways
Tip an array on its side. Nothing is added, nothing is lost.
That is why one array knows four facts.
That is why one array knows four facts.
1.Same 12 buttons, two ways. Count the rows in each. Then write the whole fact family below.
2 rows of 6
↻
6 rows of 2
2 × 6 =
6 × 2 =
12 ÷ 2 =
12 ÷ 6 =
2.Draw an array that proves 10 ÷ 5 = 2. Any orientation you like. Label your rows.
Roots of Reason
Arrays · Set 2
Name
Date
The Missing Side
Squish an array's dots together and you get area.
Division finds the side you cannot see.
Division finds the side you cannot see.
1.This rug covers 12 squares. Its short side is 3 squares. Count across the top to find the long side.
3
?
area 12
side 3
12 ÷ 3 = ?
side 3
12 ÷ 3 = ?
The long side is squares.
2.A garden covers 20 squares. One side is 5. Draw the garden on the grid: start at any corner, make one side exactly 5, and keep going until you have colored 20 squares. What is the other side?
20 ÷ 5 =
Roots of Reason
Arrays · Set 2
Name
Date
Arrays Hide Everywhere
Go on an array hunt. Egg cartons. Window panes.
Muffin tins. Chocolate bars. Find one.
Muffin tins. Chocolate bars. Find one.
1.Put a photo or drawing of YOUR array here. It must have equal rows.
or draw it here
2.Now read your array like a mathematician:
My array has rows with in each row.
That is in all.
Its division fact: ÷ =
Roots of Reason
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What Division Means · Set 2 · Grade 3
Answer Key and Teacher Notes
From a Pile to an Array (page 2)
1. Each row has 5; 15 ÷ 3 = 5 2. 12 ÷ 4 = 3 rows
Turn It Sideways (page 3)
1. 2 × 6 = 12, 6 × 2 = 12, 12 ÷ 2 = 6, 12 ÷ 6 = 2 2. Any array with 2 rows of 5 or 5 rows of 2
The Missing Side (page 4)
1. Long side = 4 squares 2. 20 ÷ 5 = 4 (any 5-by-4 rectangle on the grid counts)
Arrays Hide Everywhere (page 5)
Answers vary. Check that the rows are equal and the division fact matches the picture: total ÷ rows = per row (or total ÷ per row = rows). A standard egg carton reads 12 ÷ 2 = 6.
Page 2 is the heart of the set: turning a pile into rows IS the act of dividing. If a student arranges 15 buttons into 3 unequal rows without noticing, stop there and share out one by one before moving to page 3. The rotation on page 3 quietly buys you the whole fact-family strategy, and page 4 converts it to area, where grade 4 multiplication will pick it up.